# Properties

 Label 48.2.j.a.37.3 Level $48$ Weight $2$ Character 48.37 Analytic conductor $0.383$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$48 = 2^{4} \cdot 3$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 48.j (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.383281929702$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(i)$$ Coefficient field: 8.0.18939904.2 Defining polynomial: $$x^{8} - 4 x^{7} + 14 x^{6} - 28 x^{5} + 43 x^{4} - 44 x^{3} + 30 x^{2} - 12 x + 2$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 37.3 Root $$0.500000 + 0.691860i$$ of defining polynomial Character $$\chi$$ $$=$$ 48.37 Dual form 48.2.j.a.13.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.635665 + 1.26330i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.19186 + 1.60607i) q^{4} +(-2.68554 - 2.68554i) q^{5} +(1.34277 + 0.443806i) q^{6} +2.15894i q^{7} +(-2.78658 - 0.484753i) q^{8} -1.00000i q^{9} +O(q^{10})$$ $$q+(0.635665 + 1.26330i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.19186 + 1.60607i) q^{4} +(-2.68554 - 2.68554i) q^{5} +(1.34277 + 0.443806i) q^{6} +2.15894i q^{7} +(-2.78658 - 0.484753i) q^{8} -1.00000i q^{9} +(1.68554 - 5.09976i) q^{10} +(1.79793 + 1.79793i) q^{11} +(0.292893 + 1.97844i) q^{12} +(1.38372 - 1.38372i) q^{13} +(-2.72739 + 1.37236i) q^{14} -3.79793 q^{15} +(-1.15894 - 3.82843i) q^{16} -0.224777 q^{17} +(1.26330 - 0.635665i) q^{18} +(0.158942 - 0.158942i) q^{19} +(7.51397 - 1.11239i) q^{20} +(1.52660 + 1.52660i) q^{21} +(-1.12845 + 3.41421i) q^{22} +2.82843i q^{23} +(-2.31318 + 1.62764i) q^{24} +9.42429i q^{25} +(2.62764 + 0.868472i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-3.46742 - 2.57316i) q^{28} +(-1.85712 + 1.85712i) q^{29} +(-2.41421 - 4.79793i) q^{30} +1.84106 q^{31} +(4.09976 - 3.89769i) q^{32} +2.54266 q^{33} +(-0.142883 - 0.283962i) q^{34} +(5.79793 - 5.79793i) q^{35} +(1.60607 + 1.19186i) q^{36} +(-3.66949 - 3.66949i) q^{37} +(0.301825 + 0.0997575i) q^{38} -1.95687i q^{39} +(6.18165 + 8.78530i) q^{40} -5.88163i q^{41} +(-0.958150 + 2.89897i) q^{42} +(-7.75481 - 7.75481i) q^{43} +(-5.03049 + 0.744728i) q^{44} +(-2.68554 + 2.68554i) q^{45} +(-3.57316 + 1.79793i) q^{46} -2.82843 q^{47} +(-3.52660 - 1.88761i) q^{48} +2.33897 q^{49} +(-11.9057 + 5.99069i) q^{50} +(-0.158942 + 0.158942i) q^{51} +(0.573155 + 3.87155i) q^{52} +(7.51397 + 7.51397i) q^{53} +(0.443806 - 1.34277i) q^{54} -9.65685i q^{55} +(1.04655 - 6.01606i) q^{56} -0.224777i q^{57} +(-3.52660 - 1.16559i) q^{58} +(4.00000 + 4.00000i) q^{59} +(4.52660 - 6.09976i) q^{60} +(5.98737 - 5.98737i) q^{61} +(1.17030 + 2.32581i) q^{62} +2.15894 q^{63} +(7.53003 + 2.70160i) q^{64} -7.43208 q^{65} +(1.61628 + 3.21215i) q^{66} +(-10.4243 + 10.4243i) q^{67} +(0.267903 - 0.361009i) q^{68} +(2.00000 + 2.00000i) q^{69} +(11.0101 + 3.63899i) q^{70} -4.31788i q^{71} +(-0.484753 + 2.78658i) q^{72} -5.97474i q^{73} +(2.30310 - 6.96823i) q^{74} +(6.66398 + 6.66398i) q^{75} +(0.0658358 + 0.444708i) q^{76} +(-3.88163 + 3.88163i) q^{77} +(2.47212 - 1.24392i) q^{78} +15.0075 q^{79} +(-7.16902 + 13.3938i) q^{80} -1.00000 q^{81} +(7.43027 - 3.73875i) q^{82} +(-10.1158 + 10.1158i) q^{83} +(-4.27133 + 0.632339i) q^{84} +(0.603650 + 0.603650i) q^{85} +(4.86720 - 14.7261i) q^{86} +2.62636i q^{87} +(-4.13853 - 5.88163i) q^{88} -1.42847i q^{89} +(-5.09976 - 1.68554i) q^{90} +(2.98737 + 2.98737i) q^{91} +(-4.54266 - 3.37109i) q^{92} +(1.30182 - 1.30182i) q^{93} +(-1.79793 - 3.57316i) q^{94} -0.853690 q^{95} +(0.142883 - 5.65505i) q^{96} -16.3990 q^{97} +(1.48680 + 2.95482i) q^{98} +(1.79793 - 1.79793i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 4q^{4} - 12q^{8} + O(q^{10})$$ $$8q - 4q^{4} - 12q^{8} - 8q^{10} - 8q^{11} + 8q^{12} + 12q^{14} - 8q^{15} + 4q^{18} - 8q^{19} + 16q^{20} + 4q^{24} + 20q^{26} + 8q^{28} - 16q^{29} - 8q^{30} + 24q^{31} + 24q^{35} - 4q^{36} - 16q^{37} - 8q^{38} + 16q^{40} - 20q^{42} - 8q^{43} - 40q^{44} - 8q^{46} - 16q^{48} - 8q^{49} - 36q^{50} + 8q^{51} - 16q^{52} + 16q^{53} + 4q^{54} - 16q^{58} + 32q^{59} + 24q^{60} + 16q^{61} - 12q^{62} + 8q^{63} + 8q^{64} - 16q^{65} + 24q^{66} - 16q^{67} + 32q^{68} + 16q^{69} + 32q^{70} - 4q^{72} + 52q^{74} + 16q^{75} + 8q^{76} + 16q^{77} - 12q^{78} - 24q^{79} + 8q^{80} - 8q^{81} + 40q^{82} - 40q^{83} - 24q^{84} - 16q^{85} - 16q^{86} + 32q^{88} - 8q^{90} - 8q^{91} - 16q^{92} + 8q^{94} - 48q^{95} - 40q^{98} - 8q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$$.

 $$n$$ $$17$$ $$31$$ $$37$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{1}{4}\right)$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.635665 + 1.26330i 0.449483 + 0.893289i
$$3$$ 0.707107 0.707107i 0.408248 0.408248i
$$4$$ −1.19186 + 1.60607i −0.595930 + 0.803037i
$$5$$ −2.68554 2.68554i −1.20101 1.20101i −0.973859 0.227153i $$-0.927058\pi$$
−0.227153 0.973859i $$-0.572942\pi$$
$$6$$ 1.34277 + 0.443806i 0.548184 + 0.181183i
$$7$$ 2.15894i 0.816003i 0.912981 + 0.408002i $$0.133774\pi$$
−0.912981 + 0.408002i $$0.866226\pi$$
$$8$$ −2.78658 0.484753i −0.985204 0.171386i
$$9$$ 1.00000i 0.333333i
$$10$$ 1.68554 5.09976i 0.533016 1.61268i
$$11$$ 1.79793 + 1.79793i 0.542097 + 0.542097i 0.924143 0.382046i $$-0.124780\pi$$
−0.382046 + 0.924143i $$0.624780\pi$$
$$12$$ 0.292893 + 1.97844i 0.0845510 + 0.571126i
$$13$$ 1.38372 1.38372i 0.383775 0.383775i −0.488685 0.872460i $$-0.662523\pi$$
0.872460 + 0.488685i $$0.162523\pi$$
$$14$$ −2.72739 + 1.37236i −0.728927 + 0.366780i
$$15$$ −3.79793 −0.980622
$$16$$ −1.15894 3.82843i −0.289735 0.957107i
$$17$$ −0.224777 −0.0545165 −0.0272583 0.999628i $$-0.508678\pi$$
−0.0272583 + 0.999628i $$0.508678\pi$$
$$18$$ 1.26330 0.635665i 0.297763 0.149828i
$$19$$ 0.158942 0.158942i 0.0364637 0.0364637i −0.688640 0.725104i $$-0.741792\pi$$
0.725104 + 0.688640i $$0.241792\pi$$
$$20$$ 7.51397 1.11239i 1.68018 0.248738i
$$21$$ 1.52660 + 1.52660i 0.333132 + 0.333132i
$$22$$ −1.12845 + 3.41421i −0.240586 + 0.727913i
$$23$$ 2.82843i 0.589768i 0.955533 + 0.294884i $$0.0952810\pi$$
−0.955533 + 0.294884i $$0.904719\pi$$
$$24$$ −2.31318 + 1.62764i −0.472176 + 0.332240i
$$25$$ 9.42429i 1.88486i
$$26$$ 2.62764 + 0.868472i 0.515322 + 0.170321i
$$27$$ −0.707107 0.707107i −0.136083 0.136083i
$$28$$ −3.46742 2.57316i −0.655280 0.486281i
$$29$$ −1.85712 + 1.85712i −0.344858 + 0.344858i −0.858190 0.513332i $$-0.828411\pi$$
0.513332 + 0.858190i $$0.328411\pi$$
$$30$$ −2.41421 4.79793i −0.440773 0.875979i
$$31$$ 1.84106 0.330664 0.165332 0.986238i $$-0.447130\pi$$
0.165332 + 0.986238i $$0.447130\pi$$
$$32$$ 4.09976 3.89769i 0.724742 0.689021i
$$33$$ 2.54266 0.442620
$$34$$ −0.142883 0.283962i −0.0245043 0.0486990i
$$35$$ 5.79793 5.79793i 0.980029 0.980029i
$$36$$ 1.60607 + 1.19186i 0.267679 + 0.198643i
$$37$$ −3.66949 3.66949i −0.603260 0.603260i 0.337916 0.941176i $$-0.390278\pi$$
−0.941176 + 0.337916i $$0.890278\pi$$
$$38$$ 0.301825 + 0.0997575i 0.0489625 + 0.0161828i
$$39$$ 1.95687i 0.313351i
$$40$$ 6.18165 + 8.78530i 0.977405 + 1.38908i
$$41$$ 5.88163i 0.918557i −0.888292 0.459278i $$-0.848108\pi$$
0.888292 0.459278i $$-0.151892\pi$$
$$42$$ −0.958150 + 2.89897i −0.147846 + 0.447320i
$$43$$ −7.75481 7.75481i −1.18260 1.18260i −0.979069 0.203528i $$-0.934759\pi$$
−0.203528 0.979069i $$-0.565241\pi$$
$$44$$ −5.03049 + 0.744728i −0.758376 + 0.112272i
$$45$$ −2.68554 + 2.68554i −0.400337 + 0.400337i
$$46$$ −3.57316 + 1.79793i −0.526833 + 0.265091i
$$47$$ −2.82843 −0.412568 −0.206284 0.978492i $$-0.566137\pi$$
−0.206284 + 0.978492i $$0.566137\pi$$
$$48$$ −3.52660 1.88761i −0.509021 0.272453i
$$49$$ 2.33897 0.334139
$$50$$ −11.9057 + 5.99069i −1.68372 + 0.847212i
$$51$$ −0.158942 + 0.158942i −0.0222563 + 0.0222563i
$$52$$ 0.573155 + 3.87155i 0.0794823 + 0.536888i
$$53$$ 7.51397 + 7.51397i 1.03212 + 1.03212i 0.999467 + 0.0326567i $$0.0103968\pi$$
0.0326567 + 0.999467i $$0.489603\pi$$
$$54$$ 0.443806 1.34277i 0.0603943 0.182728i
$$55$$ 9.65685i 1.30213i
$$56$$ 1.04655 6.01606i 0.139852 0.803930i
$$57$$ 0.224777i 0.0297725i
$$58$$ −3.52660 1.16559i −0.463066 0.153050i
$$59$$ 4.00000 + 4.00000i 0.520756 + 0.520756i 0.917800 0.397044i $$-0.129964\pi$$
−0.397044 + 0.917800i $$0.629964\pi$$
$$60$$ 4.52660 6.09976i 0.584382 0.787475i
$$61$$ 5.98737 5.98737i 0.766604 0.766604i −0.210903 0.977507i $$-0.567640\pi$$
0.977507 + 0.210903i $$0.0676404\pi$$
$$62$$ 1.17030 + 2.32581i 0.148628 + 0.295378i
$$63$$ 2.15894 0.272001
$$64$$ 7.53003 + 2.70160i 0.941254 + 0.337700i
$$65$$ −7.43208 −0.921836
$$66$$ 1.61628 + 3.21215i 0.198950 + 0.395388i
$$67$$ −10.4243 + 10.4243i −1.27353 + 1.27353i −0.329307 + 0.944223i $$0.606815\pi$$
−0.944223 + 0.329307i $$0.893185\pi$$
$$68$$ 0.267903 0.361009i 0.0324880 0.0437788i
$$69$$ 2.00000 + 2.00000i 0.240772 + 0.240772i
$$70$$ 11.0101 + 3.63899i 1.31596 + 0.434943i
$$71$$ 4.31788i 0.512438i −0.966619 0.256219i $$-0.917523\pi$$
0.966619 0.256219i $$-0.0824769\pi$$
$$72$$ −0.484753 + 2.78658i −0.0571287 + 0.328401i
$$73$$ 5.97474i 0.699290i −0.936882 0.349645i $$-0.886302\pi$$
0.936882 0.349645i $$-0.113698\pi$$
$$74$$ 2.30310 6.96823i 0.267730 0.810040i
$$75$$ 6.66398 + 6.66398i 0.769490 + 0.769490i
$$76$$ 0.0658358 + 0.444708i 0.00755188 + 0.0510115i
$$77$$ −3.88163 + 3.88163i −0.442353 + 0.442353i
$$78$$ 2.47212 1.24392i 0.279913 0.140846i
$$79$$ 15.0075 1.68848 0.844239 0.535966i $$-0.180053\pi$$
0.844239 + 0.535966i $$0.180053\pi$$
$$80$$ −7.16902 + 13.3938i −0.801521 + 1.49747i
$$81$$ −1.00000 −0.111111
$$82$$ 7.43027 3.73875i 0.820536 0.412876i
$$83$$ −10.1158 + 10.1158i −1.11036 + 1.11036i −0.117253 + 0.993102i $$0.537409\pi$$
−0.993102 + 0.117253i $$0.962591\pi$$
$$84$$ −4.27133 + 0.632339i −0.466040 + 0.0689939i
$$85$$ 0.603650 + 0.603650i 0.0654750 + 0.0654750i
$$86$$ 4.86720 14.7261i 0.524843 1.58796i
$$87$$ 2.62636i 0.281575i
$$88$$ −4.13853 5.88163i −0.441168 0.626984i
$$89$$ 1.42847i 0.151417i −0.997130 0.0757086i $$-0.975878\pi$$
0.997130 0.0757086i $$-0.0241219\pi$$
$$90$$ −5.09976 1.68554i −0.537562 0.177672i
$$91$$ 2.98737 + 2.98737i 0.313161 + 0.313161i
$$92$$ −4.54266 3.37109i −0.473605 0.351460i
$$93$$ 1.30182 1.30182i 0.134993 0.134993i
$$94$$ −1.79793 3.57316i −0.185443 0.368543i
$$95$$ −0.853690 −0.0875867
$$96$$ 0.142883 5.65505i 0.0145830 0.577166i
$$97$$ −16.3990 −1.66507 −0.832535 0.553973i $$-0.813111\pi$$
−0.832535 + 0.553973i $$0.813111\pi$$
$$98$$ 1.48680 + 2.95482i 0.150190 + 0.298482i
$$99$$ 1.79793 1.79793i 0.180699 0.180699i
$$100$$ −15.1361 11.2324i −1.51361 1.12324i
$$101$$ 0.0818942 + 0.0818942i 0.00814878 + 0.00814878i 0.711169 0.703021i $$-0.248166\pi$$
−0.703021 + 0.711169i $$0.748166\pi$$
$$102$$ −0.301825 0.0997575i −0.0298851 0.00987746i
$$103$$ 13.3507i 1.31548i 0.753245 + 0.657740i $$0.228488\pi$$
−0.753245 + 0.657740i $$0.771512\pi$$
$$104$$ −4.52660 + 3.18508i −0.443870 + 0.312323i
$$105$$ 8.19951i 0.800191i
$$106$$ −4.71604 + 14.2688i −0.458062 + 1.38591i
$$107$$ −7.27798 7.27798i −0.703589 0.703589i 0.261590 0.965179i $$-0.415753\pi$$
−0.965179 + 0.261590i $$0.915753\pi$$
$$108$$ 1.97844 0.292893i 0.190375 0.0281837i
$$109$$ −7.04057 + 7.04057i −0.674365 + 0.674365i −0.958719 0.284355i $$-0.908221\pi$$
0.284355 + 0.958719i $$0.408221\pi$$
$$110$$ 12.1995 6.13853i 1.16318 0.585285i
$$111$$ −5.18944 −0.492559
$$112$$ 8.26535 2.50209i 0.781002 0.236425i
$$113$$ 18.8486 1.77313 0.886563 0.462608i $$-0.153086\pi$$
0.886563 + 0.462608i $$0.153086\pi$$
$$114$$ 0.283962 0.142883i 0.0265954 0.0133822i
$$115$$ 7.59587 7.59587i 0.708318 0.708318i
$$116$$ −0.769243 5.19609i −0.0714224 0.482445i
$$117$$ −1.38372 1.38372i −0.127925 0.127925i
$$118$$ −2.51054 + 7.59587i −0.231114 + 0.699256i
$$119$$ 0.485281i 0.0444857i
$$120$$ 10.5832 + 1.84106i 0.966113 + 0.168065i
$$121$$ 4.53488i 0.412261i
$$122$$ 11.3698 + 3.75789i 1.02937 + 0.340223i
$$123$$ −4.15894 4.15894i −0.374999 0.374999i
$$124$$ −2.19428 + 2.95687i −0.197052 + 0.265535i
$$125$$ 11.8816 11.8816i 1.06273 1.06273i
$$126$$ 1.37236 + 2.72739i 0.122260 + 0.242976i
$$127$$ −3.81580 −0.338597 −0.169299 0.985565i $$-0.554150\pi$$
−0.169299 + 0.985565i $$0.554150\pi$$
$$128$$ 1.37364 + 11.2300i 0.121414 + 0.992602i
$$129$$ −10.9670 −0.965586
$$130$$ −4.72431 9.38895i −0.414350 0.823465i
$$131$$ −0.767438 + 0.767438i −0.0670514 + 0.0670514i −0.739837 0.672786i $$-0.765098\pi$$
0.672786 + 0.739837i $$0.265098\pi$$
$$132$$ −3.03049 + 4.08370i −0.263771 + 0.355440i
$$133$$ 0.343146 + 0.343146i 0.0297545 + 0.0297545i
$$134$$ −19.7954 6.54266i −1.71006 0.565200i
$$135$$ 3.79793i 0.326874i
$$136$$ 0.626360 + 0.108961i 0.0537099 + 0.00934337i
$$137$$ 5.31010i 0.453672i 0.973933 + 0.226836i $$0.0728382\pi$$
−0.973933 + 0.226836i $$0.927162\pi$$
$$138$$ −1.25527 + 3.79793i −0.106856 + 0.323301i
$$139$$ 8.76744 + 8.76744i 0.743644 + 0.743644i 0.973277 0.229633i $$-0.0737526\pi$$
−0.229633 + 0.973277i $$0.573753\pi$$
$$140$$ 2.40158 + 16.2222i 0.202971 + 1.37103i
$$141$$ −2.00000 + 2.00000i −0.168430 + 0.168430i
$$142$$ 5.45479 2.74473i 0.457756 0.230332i
$$143$$ 4.97567 0.416086
$$144$$ −3.82843 + 1.15894i −0.319036 + 0.0965785i
$$145$$ 9.97474 0.828357
$$146$$ 7.54789 3.79793i 0.624668 0.314319i
$$147$$ 1.65390 1.65390i 0.136412 0.136412i
$$148$$ 10.2670 1.51995i 0.843940 0.124939i
$$149$$ −1.02869 1.02869i −0.0842735 0.0842735i 0.663713 0.747987i $$-0.268979\pi$$
−0.747987 + 0.663713i $$0.768979\pi$$
$$150$$ −4.18255 + 12.6547i −0.341504 + 1.03325i
$$151$$ 2.03696i 0.165766i −0.996559 0.0828829i $$-0.973587\pi$$
0.996559 0.0828829i $$-0.0264127\pi$$
$$152$$ −0.519951 + 0.365856i −0.0421736 + 0.0296748i
$$153$$ 0.224777i 0.0181722i
$$154$$ −7.37109 2.43625i −0.593979 0.196319i
$$155$$ −4.94424 4.94424i −0.397131 0.397131i
$$156$$ 3.14288 + 2.33232i 0.251632 + 0.186735i
$$157$$ 6.09378 6.09378i 0.486336 0.486336i −0.420812 0.907148i $$-0.638255\pi$$
0.907148 + 0.420812i $$0.138255\pi$$
$$158$$ 9.53976 + 18.9590i 0.758943 + 1.50830i
$$159$$ 10.6264 0.842725
$$160$$ −21.4775 0.542661i −1.69795 0.0429011i
$$161$$ −6.10641 −0.481252
$$162$$ −0.635665 1.26330i −0.0499426 0.0992543i
$$163$$ 3.43692 3.43692i 0.269201 0.269201i −0.559577 0.828778i $$-0.689037\pi$$
0.828778 + 0.559577i $$0.189037\pi$$
$$164$$ 9.44633 + 7.01008i 0.737634 + 0.547395i
$$165$$ −6.82843 6.82843i −0.531592 0.531592i
$$166$$ −19.2096 6.34905i −1.49095 0.492782i
$$167$$ 21.7023i 1.67937i −0.543072 0.839686i $$-0.682739\pi$$
0.543072 0.839686i $$-0.317261\pi$$
$$168$$ −3.51397 4.99402i −0.271109 0.385297i
$$169$$ 9.17064i 0.705434i
$$170$$ −0.378872 + 1.14631i −0.0290582 + 0.0879180i
$$171$$ −0.158942 0.158942i −0.0121546 0.0121546i
$$172$$ 21.6974 3.21215i 1.65441 0.244924i
$$173$$ −8.74653 + 8.74653i −0.664987 + 0.664987i −0.956551 0.291565i $$-0.905824\pi$$
0.291565 + 0.956551i $$0.405824\pi$$
$$174$$ −3.31788 + 1.66949i −0.251528 + 0.126563i
$$175$$ −20.3465 −1.53805
$$176$$ 4.79956 8.96695i 0.361780 0.675910i
$$177$$ 5.65685 0.425195
$$178$$ 1.80458 0.908027i 0.135259 0.0680595i
$$179$$ 8.23163 8.23163i 0.615261 0.615261i −0.329051 0.944312i $$-0.606729\pi$$
0.944312 + 0.329051i $$0.106729\pi$$
$$180$$ −1.11239 7.51397i −0.0829126 0.560058i
$$181$$ 6.72269 + 6.72269i 0.499694 + 0.499694i 0.911343 0.411649i $$-0.135047\pi$$
−0.411649 + 0.911343i $$0.635047\pi$$
$$182$$ −1.87498 + 5.67291i −0.138983 + 0.420504i
$$183$$ 8.46742i 0.625930i
$$184$$ 1.37109 7.88163i 0.101078 0.581042i
$$185$$ 19.7091i 1.44904i
$$186$$ 2.47212 + 0.817072i 0.181265 + 0.0599106i
$$187$$ −0.404135 0.404135i −0.0295533 0.0295533i
$$188$$ 3.37109 4.54266i 0.245862 0.331308i
$$189$$ 1.52660 1.52660i 0.111044 0.111044i
$$190$$ −0.542661 1.07847i −0.0393687 0.0782402i
$$191$$ −20.8032 −1.50526 −0.752632 0.658441i $$-0.771216\pi$$
−0.752632 + 0.658441i $$0.771216\pi$$
$$192$$ 7.23486 3.41421i 0.522131 0.246400i
$$193$$ 14.1454 1.01821 0.509103 0.860705i $$-0.329977\pi$$
0.509103 + 0.860705i $$0.329977\pi$$
$$194$$ −10.4243 20.7169i −0.748421 1.48739i
$$195$$ −5.25527 + 5.25527i −0.376338 + 0.376338i
$$196$$ −2.78772 + 3.75656i −0.199123 + 0.268326i
$$197$$ −2.42865 2.42865i −0.173034 0.173034i 0.615277 0.788311i $$-0.289044\pi$$
−0.788311 + 0.615277i $$0.789044\pi$$
$$198$$ 3.41421 + 1.12845i 0.242638 + 0.0801952i
$$199$$ 0.306182i 0.0217047i 0.999941 + 0.0108523i $$0.00345447\pi$$
−0.999941 + 0.0108523i $$0.996546\pi$$
$$200$$ 4.56845 26.2615i 0.323038 1.85697i
$$201$$ 14.7422i 1.03983i
$$202$$ −0.0513998 + 0.155514i −0.00361648 + 0.0109420i
$$203$$ −4.00941 4.00941i −0.281405 0.281405i
$$204$$ −0.0658358 0.444708i −0.00460943 0.0311358i
$$205$$ −15.7954 + 15.7954i −1.10320 + 1.10320i
$$206$$ −16.8659 + 8.48656i −1.17510 + 0.591286i
$$207$$ 2.82843 0.196589
$$208$$ −6.90112 3.69382i −0.478506 0.256120i
$$209$$ 0.571533 0.0395337
$$210$$ 10.3585 5.21215i 0.714801 0.359672i
$$211$$ 7.23256 7.23256i 0.497910 0.497910i −0.412877 0.910787i $$-0.635476\pi$$
0.910787 + 0.412877i $$0.135476\pi$$
$$212$$ −21.0236 + 3.11239i −1.44391 + 0.213760i
$$213$$ −3.05320 3.05320i −0.209202 0.209202i
$$214$$ 4.56792 13.8206i 0.312257 0.944760i
$$215$$ 41.6517i 2.84063i
$$216$$ 1.62764 + 2.31318i 0.110747 + 0.157392i
$$217$$ 3.97474i 0.269823i
$$218$$ −13.3698 4.41892i −0.905518 0.299287i
$$219$$ −4.22478 4.22478i −0.285484 0.285484i
$$220$$ 15.5096 + 11.5096i 1.04566 + 0.775978i
$$221$$ −0.311029 + 0.311029i −0.0209221 + 0.0209221i
$$222$$ −3.29874 6.55582i −0.221397 0.439998i
$$223$$ −1.71908 −0.115118 −0.0575591 0.998342i $$-0.518332\pi$$
−0.0575591 + 0.998342i $$0.518332\pi$$
$$224$$ 8.41489 + 8.85114i 0.562243 + 0.591391i
$$225$$ 9.42429 0.628286
$$226$$ 11.9814 + 23.8114i 0.796990 + 1.58391i
$$227$$ 10.1158 10.1158i 0.671410 0.671410i −0.286631 0.958041i $$-0.592535\pi$$
0.958041 + 0.286631i $$0.0925353\pi$$
$$228$$ 0.361009 + 0.267903i 0.0239084 + 0.0177423i
$$229$$ −12.0195 12.0195i −0.794270 0.794270i 0.187915 0.982185i $$-0.439827\pi$$
−0.982185 + 0.187915i $$0.939827\pi$$
$$230$$ 14.4243 + 4.76744i 0.951110 + 0.314356i
$$231$$ 5.48946i 0.361180i
$$232$$ 6.07524 4.27476i 0.398859 0.280652i
$$233$$ 13.3779i 0.876418i −0.898873 0.438209i $$-0.855613\pi$$
0.898873 0.438209i $$-0.144387\pi$$
$$234$$ 0.868472 2.62764i 0.0567738 0.171774i
$$235$$ 7.59587 + 7.59587i 0.495500 + 0.495500i
$$236$$ −11.1917 + 1.65685i −0.728520 + 0.107852i
$$237$$ 10.6119 10.6119i 0.689319 0.689319i
$$238$$ 0.613057 0.308476i 0.0397386 0.0199956i
$$239$$ 13.3675 0.864670 0.432335 0.901713i $$-0.357690\pi$$
0.432335 + 0.901713i $$0.357690\pi$$
$$240$$ 4.40158 + 14.5401i 0.284121 + 0.938560i
$$241$$ 0.211474 0.0136222 0.00681112 0.999977i $$-0.497832\pi$$
0.00681112 + 0.999977i $$0.497832\pi$$
$$242$$ 5.72891 2.88266i 0.368269 0.185305i
$$243$$ −0.707107 + 0.707107i −0.0453609 + 0.0453609i
$$244$$ 2.48005 + 16.7523i 0.158769 + 1.07245i
$$245$$ −6.28141 6.28141i −0.401305 0.401305i
$$246$$ 2.61030 7.89769i 0.166427 0.503538i
$$247$$ 0.439861i 0.0279877i
$$248$$ −5.13025 0.892458i −0.325771 0.0566711i
$$249$$ 14.3059i 0.906601i
$$250$$ 22.5628 + 7.45734i 1.42700 + 0.471644i
$$251$$ 10.4337 + 10.4337i 0.658569 + 0.658569i 0.955041 0.296472i $$-0.0958102\pi$$
−0.296472 + 0.955041i $$0.595810\pi$$
$$252$$ −2.57316 + 3.46742i −0.162094 + 0.218427i
$$253$$ −5.08532 + 5.08532i −0.319711 + 0.319711i
$$254$$ −2.42557 4.82050i −0.152194 0.302465i
$$255$$ 0.853690 0.0534601
$$256$$ −13.3137 + 8.87385i −0.832107 + 0.554615i
$$257$$ −0.742176 −0.0462957 −0.0231478 0.999732i $$-0.507369\pi$$
−0.0231478 + 0.999732i $$0.507369\pi$$
$$258$$ −6.97131 13.8546i −0.434015 0.862548i
$$259$$ 7.92221 7.92221i 0.492262 0.492262i
$$260$$ 8.85799 11.9365i 0.549349 0.740268i
$$261$$ 1.85712 + 1.85712i 0.114953 + 0.114953i
$$262$$ −1.45734 0.481672i −0.0900347 0.0297578i
$$263$$ 5.48435i 0.338180i 0.985601 + 0.169090i $$0.0540828\pi$$
−0.985601 + 0.169090i $$0.945917\pi$$
$$264$$ −7.08532 1.23256i −0.436071 0.0758589i
$$265$$ 40.3582i 2.47918i
$$266$$ −0.215371 + 0.651622i −0.0132052 + 0.0399535i
$$267$$ −1.01008 1.01008i −0.0618158 0.0618158i
$$268$$ −4.31788 29.1665i −0.263757 1.78163i
$$269$$ 14.4741 14.4741i 0.882500 0.882500i −0.111289 0.993788i $$-0.535498\pi$$
0.993788 + 0.111289i $$0.0354978\pi$$
$$270$$ −4.79793 + 2.41421i −0.291993 + 0.146924i
$$271$$ −14.0370 −0.852685 −0.426342 0.904562i $$-0.640198\pi$$
−0.426342 + 0.904562i $$0.640198\pi$$
$$272$$ 0.260504 + 0.860544i 0.0157954 + 0.0521781i
$$273$$ 4.22478 0.255695
$$274$$ −6.70825 + 3.37545i −0.405260 + 0.203918i
$$275$$ −16.9442 + 16.9442i −1.02178 + 1.02178i
$$276$$ −5.59587 + 0.828427i −0.336832 + 0.0498655i
$$277$$ 9.49013 + 9.49013i 0.570207 + 0.570207i 0.932186 0.361980i $$-0.117899\pi$$
−0.361980 + 0.932186i $$0.617899\pi$$
$$278$$ −5.50276 + 16.6491i −0.330034 + 0.998545i
$$279$$ 1.84106i 0.110221i
$$280$$ −18.9670 + 13.3458i −1.13349 + 0.797566i
$$281$$ 3.89359i 0.232272i 0.993233 + 0.116136i $$0.0370509\pi$$
−0.993233 + 0.116136i $$0.962949\pi$$
$$282$$ −3.79793 1.25527i −0.226164 0.0747504i
$$283$$ −12.4853 12.4853i −0.742173 0.742173i 0.230823 0.972996i $$-0.425858\pi$$
−0.972996 + 0.230823i $$0.925858\pi$$
$$284$$ 6.93484 + 5.14631i 0.411507 + 0.305377i
$$285$$ −0.603650 + 0.603650i −0.0357571 + 0.0357571i
$$286$$ 3.16286 + 6.28577i 0.187024 + 0.371685i
$$287$$ 12.6981 0.749545
$$288$$ −3.89769 4.09976i −0.229674 0.241581i
$$289$$ −16.9495 −0.997028
$$290$$ 6.34059 + 12.6011i 0.372332 + 0.739962i
$$291$$ −11.5959 + 11.5959i −0.679762 + 0.679762i
$$292$$ 9.59587 + 7.12105i 0.561556 + 0.416728i
$$293$$ −11.1553 11.1553i −0.651697 0.651697i 0.301704 0.953402i $$-0.402444\pi$$
−0.953402 + 0.301704i $$0.902444\pi$$
$$294$$ 3.14070 + 1.03805i 0.183170 + 0.0605402i
$$295$$ 21.4844i 1.25087i
$$296$$ 8.44651 + 12.0041i 0.490944 + 0.697724i
$$297$$ 2.54266i 0.147540i
$$298$$ 0.645643 1.95345i 0.0374011 0.113160i
$$299$$ 3.91375 + 3.91375i 0.226338 + 0.226338i
$$300$$ −18.6454 + 2.76031i −1.07649 + 0.159367i
$$301$$ 16.7422 16.7422i 0.965003 0.965003i
$$302$$ 2.57330 1.29483i 0.148077 0.0745089i
$$303$$ 0.115816 0.00665345
$$304$$ −0.792701 0.424292i −0.0454645 0.0243348i
$$305$$ −32.1587 −1.84140
$$306$$ −0.283962 + 0.142883i −0.0162330 + 0.00816809i
$$307$$ −5.40320 + 5.40320i −0.308377 + 0.308377i −0.844280 0.535903i $$-0.819971\pi$$
0.535903 + 0.844280i $$0.319971\pi$$
$$308$$ −1.60782 10.8605i −0.0916143 0.618837i
$$309$$ 9.44035 + 9.44035i 0.537043 + 0.537043i
$$310$$ 3.10318 9.38895i 0.176249 0.533257i
$$311$$ 24.1623i 1.37012i −0.728488 0.685059i $$-0.759776\pi$$
0.728488 0.685059i $$-0.240224\pi$$
$$312$$ −0.948600 + 5.45298i −0.0537039 + 0.308714i
$$313$$ 16.6105i 0.938881i −0.882964 0.469441i $$-0.844456\pi$$
0.882964 0.469441i $$-0.155544\pi$$
$$314$$ 11.5719 + 3.82467i 0.653039 + 0.215839i
$$315$$ −5.79793 5.79793i −0.326676 0.326676i
$$316$$ −17.8869 + 24.1032i −1.00621 + 1.35591i
$$317$$ 1.81170 1.81170i 0.101755 0.101755i −0.654397 0.756152i $$-0.727077\pi$$
0.756152 + 0.654397i $$0.227077\pi$$
$$318$$ 6.75481 + 13.4243i 0.378791 + 0.752797i
$$319$$ −6.67794 −0.373893
$$320$$ −12.9670 27.4775i −0.724875 1.53604i
$$321$$ −10.2926 −0.574478
$$322$$ −3.88163 7.71423i −0.216315 0.429897i
$$323$$ −0.0357265 + 0.0357265i −0.00198788 + 0.00198788i
$$324$$ 1.19186 1.60607i 0.0662144 0.0892263i
$$325$$ 13.0406 + 13.0406i 0.723361 + 0.723361i
$$326$$ 6.52660 + 2.15714i 0.361475 + 0.119473i
$$327$$ 9.95687i 0.550616i
$$328$$ −2.85114 + 16.3896i −0.157428 + 0.904966i
$$329$$ 6.10641i 0.336657i
$$330$$ 4.28577 12.9670i 0.235924 0.713807i
$$331$$ 13.5252 + 13.5252i 0.743411 + 0.743411i 0.973233 0.229822i $$-0.0738142\pi$$
−0.229822 + 0.973233i $$0.573814\pi$$
$$332$$ −4.19011 28.3034i −0.229962 1.55335i
$$333$$ −3.66949 + 3.66949i −0.201087 + 0.201087i
$$334$$ 27.4165 13.7954i 1.50016 0.754850i
$$335$$ 55.9898 3.05905
$$336$$ 4.07524 7.61373i 0.222323 0.415363i
$$337$$ −1.12615 −0.0613454 −0.0306727 0.999529i $$-0.509765\pi$$
−0.0306727 + 0.999529i $$0.509765\pi$$
$$338$$ −11.5853 + 5.82946i −0.630156 + 0.317081i
$$339$$ 13.3280 13.3280i 0.723876 0.723876i
$$340$$ −1.68897 + 0.250040i −0.0915973 + 0.0135603i
$$341$$ 3.31010 + 3.31010i 0.179252 + 0.179252i
$$342$$ 0.0997575 0.301825i 0.00539427 0.0163208i
$$343$$ 20.1623i 1.08866i
$$344$$ 17.8502 + 25.3685i 0.962419 + 1.36778i
$$345$$ 10.7422i 0.578339i
$$346$$ −16.6094 5.48964i −0.892925 0.295125i
$$347$$ 20.7938 + 20.7938i 1.11627 + 1.11627i 0.992284 + 0.123983i $$0.0395669\pi$$
0.123983 + 0.992284i $$0.460433\pi$$
$$348$$ −4.21813 3.13025i −0.226115 0.167799i
$$349$$ −19.2855 + 19.2855i −1.03233 + 1.03233i −0.0328700 + 0.999460i $$0.510465\pi$$
−0.999460 + 0.0328700i $$0.989535\pi$$
$$350$$ −12.9336 25.7038i −0.691328 1.37392i
$$351$$ −1.95687 −0.104450
$$352$$ 14.3789 + 0.363303i 0.766396 + 0.0193641i
$$353$$ 25.5908 1.36206 0.681029 0.732256i $$-0.261533\pi$$
0.681029 + 0.732256i $$0.261533\pi$$
$$354$$ 3.59587 + 7.14631i 0.191118 + 0.379822i
$$355$$ −11.5959 + 11.5959i −0.615445 + 0.615445i
$$356$$ 2.29422 + 1.70253i 0.121594 + 0.0902340i
$$357$$ −0.343146 0.343146i −0.0181612 0.0181612i
$$358$$ 15.6316 + 5.16647i 0.826155 + 0.273056i
$$359$$ 3.77296i 0.199129i 0.995031 + 0.0995645i $$0.0317450\pi$$
−0.995031 + 0.0995645i $$0.968255\pi$$
$$360$$ 8.78530 6.18165i 0.463026 0.325802i
$$361$$ 18.9495i 0.997341i
$$362$$ −4.21940 + 12.7662i −0.221767 + 0.670975i
$$363$$ −3.20664 3.20664i −0.168305 0.168305i
$$364$$ −8.35846 + 1.23741i −0.438102 + 0.0648578i
$$365$$ −16.0454 + 16.0454i −0.839856 + 0.839856i
$$366$$ 10.6969 5.38244i 0.559136 0.281345i
$$367$$ −27.4474 −1.43274 −0.716371 0.697720i $$-0.754198\pi$$
−0.716371 + 0.697720i $$0.754198\pi$$
$$368$$ 10.8284 3.27798i 0.564471 0.170877i
$$369$$ −5.88163 −0.306186
$$370$$ −24.8986 + 12.5284i −1.29441 + 0.651321i
$$371$$ −16.2222 + 16.2222i −0.842216 + 0.842216i
$$372$$ 0.539234 + 3.64242i 0.0279580 + 0.188851i
$$373$$ 12.6231 + 12.6231i 0.653601 + 0.653601i 0.953858 0.300257i $$-0.0970725\pi$$
−0.300257 + 0.953858i $$0.597072\pi$$
$$374$$ 0.253649 0.767438i 0.0131159 0.0396833i
$$375$$ 16.8032i 0.867712i
$$376$$ 7.88163 + 1.37109i 0.406464 + 0.0707085i
$$377$$ 5.13946i 0.264695i
$$378$$ 2.89897 + 0.958150i 0.149107 + 0.0492819i
$$379$$ −11.6686 11.6686i −0.599373 0.599373i 0.340772 0.940146i $$-0.389311\pi$$
−0.940146 + 0.340772i $$0.889311\pi$$
$$380$$ 1.01748 1.37109i 0.0521955 0.0703353i
$$381$$ −2.69818 + 2.69818i −0.138232 + 0.138232i
$$382$$ −13.2238 26.2807i −0.676591 1.34464i
$$383$$ −17.1885 −0.878291 −0.439145 0.898416i $$-0.644719\pi$$
−0.439145 + 0.898416i $$0.644719\pi$$
$$384$$ 8.91213 + 6.96951i 0.454795 + 0.355661i
$$385$$ 20.8486 1.06254
$$386$$ 8.99173 + 17.8699i 0.457667 + 0.909553i
$$387$$ −7.75481 + 7.75481i −0.394199 + 0.394199i
$$388$$ 19.5453 26.3380i 0.992264 1.33711i
$$389$$ −1.88238 1.88238i −0.0954404 0.0954404i 0.657774 0.753215i $$-0.271498\pi$$
−0.753215 + 0.657774i $$0.771498\pi$$
$$390$$ −9.97958 3.29840i −0.505336 0.167021i
$$391$$ 0.635767i 0.0321521i
$$392$$ −6.51772 1.13382i −0.329195 0.0572667i
$$393$$ 1.08532i 0.0547472i
$$394$$ 1.52431 4.61192i 0.0767935 0.232345i
$$395$$ −40.3034 40.3034i −2.02788 2.02788i
$$396$$ 0.744728 + 5.03049i 0.0374240 + 0.252792i
$$397$$ 8.41166 8.41166i 0.422169 0.422169i −0.463781 0.885950i $$-0.653507\pi$$
0.885950 + 0.463781i $$0.153507\pi$$
$$398$$ −0.386800 + 0.194629i −0.0193885 + 0.00975588i
$$399$$ 0.485281 0.0242945
$$400$$ 36.0802 10.9222i 1.80401 0.546110i
$$401$$ 1.12389 0.0561242 0.0280621 0.999606i $$-0.491066\pi$$
0.0280621 + 0.999606i $$0.491066\pi$$
$$402$$ −18.6238 + 9.37109i −0.928871 + 0.467387i
$$403$$ 2.54751 2.54751i 0.126900 0.126900i
$$404$$ −0.229135 + 0.0339217i −0.0113999 + 0.00168767i
$$405$$ 2.68554 + 2.68554i 0.133446 + 0.133446i
$$406$$ 2.51645 7.61373i 0.124889 0.377863i
$$407$$ 13.1950i 0.654051i
$$408$$ 0.519951 0.365856i 0.0257414 0.0181126i
$$409$$ 13.7211i 0.678464i 0.940703 + 0.339232i $$0.110167\pi$$
−0.940703 + 0.339232i $$0.889833\pi$$
$$410$$ −29.9949 9.91375i −1.48134 0.489605i
$$411$$ 3.75481 + 3.75481i 0.185211 + 0.185211i
$$412$$ −21.4422 15.9121i −1.05638 0.783934i
$$413$$ −8.63577 + 8.63577i −0.424938 + 0.424938i
$$414$$ 1.79793 + 3.57316i 0.0883636 + 0.175611i
$$415$$ 54.3329 2.66710
$$416$$ 0.279604 11.0662i 0.0137087 0.542566i
$$417$$ 12.3990 0.607183
$$418$$ 0.363303 + 0.722018i 0.0177698 + 0.0353151i
$$419$$ −9.30755 + 9.30755i −0.454703 + 0.454703i −0.896912 0.442209i $$-0.854195\pi$$
0.442209 + 0.896912i $$0.354195\pi$$
$$420$$ 13.1690 + 9.77267i 0.642582 + 0.476857i
$$421$$ 8.44378 + 8.44378i 0.411525 + 0.411525i 0.882269 0.470745i $$-0.156015\pi$$
−0.470745 + 0.882269i $$0.656015\pi$$
$$422$$ 13.7344 + 4.53942i 0.668580 + 0.220975i
$$423$$ 2.82843i 0.137523i
$$424$$ −17.2958 24.5807i −0.839960 1.19374i
$$425$$ 2.11837i 0.102756i
$$426$$ 1.91630 5.79793i 0.0928451 0.280911i
$$427$$ 12.9264 + 12.9264i 0.625551 + 0.625551i
$$428$$ 20.3633 3.01464i 0.984297 0.145718i
$$429$$ 3.51833 3.51833i 0.169866 0.169866i
$$430$$ −52.6187 + 26.4766i −2.53750 + 1.27681i
$$431$$ −30.6054 −1.47421 −0.737105 0.675778i $$-0.763808\pi$$
−0.737105 + 0.675778i $$0.763808\pi$$
$$432$$ −1.88761 + 3.52660i −0.0908177 + 0.169674i
$$433$$ −15.3137 −0.735930 −0.367965 0.929840i $$-0.619945\pi$$
−0.367965 + 0.929840i $$0.619945\pi$$
$$434$$ −5.02129 + 2.52660i −0.241030 + 0.121281i
$$435$$ 7.05320 7.05320i 0.338175 0.338175i
$$436$$ −2.91630 19.6991i −0.139665 0.943413i
$$437$$ 0.449555 + 0.449555i 0.0215051 + 0.0215051i
$$438$$ 2.65162 8.02271i 0.126699 0.383340i
$$439$$ 33.3676i 1.59255i −0.604936 0.796274i $$-0.706801\pi$$
0.604936 0.796274i $$-0.293199\pi$$
$$440$$ −4.68119 + 26.9096i −0.223167 + 1.28286i
$$441$$ 2.33897i 0.111380i
$$442$$ −0.590633 0.195213i −0.0280936 0.00928533i
$$443$$ 2.28832 + 2.28832i 0.108721 + 0.108721i 0.759375 0.650653i $$-0.225505\pi$$
−0.650653 + 0.759375i $$0.725505\pi$$
$$444$$ 6.18508 8.33461i 0.293531 0.395543i
$$445$$ −3.83621 + 3.83621i −0.181854 + 0.181854i
$$446$$ −1.09276 2.17172i −0.0517437 0.102834i
$$447$$ −1.45479 −0.0688091
$$448$$ −5.83260 + 16.2569i −0.275565 + 0.768066i
$$449$$ −27.4165 −1.29387 −0.646933 0.762547i $$-0.723948\pi$$
−0.646933 + 0.762547i $$0.723948\pi$$
$$450$$ 5.99069 + 11.9057i 0.282404 + 0.561241i
$$451$$ 10.5748 10.5748i 0.497947 0.497947i
$$452$$ −22.4649 + 30.2722i −1.05666 + 1.42388i
$$453$$ −1.44035 1.44035i −0.0676736 0.0676736i
$$454$$ 19.2096 + 6.34905i 0.901551 + 0.297976i
$$455$$ 16.0454i 0.752221i
$$456$$ −0.108961 + 0.626360i −0.00510259 + 0.0293320i
$$457$$ 10.9147i 0.510567i 0.966866 + 0.255284i $$0.0821688\pi$$
−0.966866 + 0.255284i $$0.917831\pi$$
$$458$$ 7.54386 22.8246i 0.352501 1.06652i
$$459$$ 0.158942 + 0.158942i 0.00741876 + 0.00741876i
$$460$$ 3.14631 + 21.2527i 0.146697 + 0.990913i
$$461$$ 17.8319 17.8319i 0.830512 0.830512i −0.157075 0.987587i $$-0.550206\pi$$
0.987587 + 0.157075i $$0.0502063\pi$$
$$462$$ −6.93484 + 3.48946i −0.322638 + 0.162344i
$$463$$ 22.4937 1.04537 0.522686 0.852525i $$-0.324930\pi$$
0.522686 + 0.852525i $$0.324930\pi$$
$$464$$ 9.26213 + 4.95755i 0.429983 + 0.230148i
$$465$$ −6.99222 −0.324256
$$466$$ 16.9004 8.50389i 0.782895 0.393935i
$$467$$ 24.2171 24.2171i 1.12063 1.12063i 0.128989 0.991646i $$-0.458827\pi$$
0.991646 0.128989i $$-0.0411731\pi$$
$$468$$ 3.87155 0.573155i 0.178963 0.0264941i
$$469$$ −22.5054 22.5054i −1.03920 1.03920i
$$470$$ −4.76744 + 14.4243i −0.219906 + 0.665343i
$$471$$ 8.61790i 0.397092i
$$472$$ −9.20730 13.0853i −0.423800 0.602301i
$$473$$ 27.8852i 1.28216i
$$474$$ 20.1517 + 6.66042i 0.925598 + 0.305923i
$$475$$ 1.49791 + 1.49791i 0.0687289 + 0.0687289i
$$476$$ 0.779397 + 0.578387i 0.0357236 + 0.0265103i
$$477$$ 7.51397 7.51397i 0.344041 0.344041i
$$478$$ 8.49724 + 16.8872i 0.388655 + 0.772400i
$$479$$ −36.2362 −1.65568 −0.827838 0.560968i $$-0.810429\pi$$
−0.827838 + 0.560968i $$0.810429\pi$$
$$480$$ −15.5706 + 14.8032i −0.710698 + 0.675669i
$$481$$ −10.1551 −0.463032
$$482$$ 0.134427 + 0.267156i 0.00612297 + 0.0121686i
$$483$$ −4.31788 + 4.31788i −0.196470 + 0.196470i
$$484$$ 7.28334 + 5.40494i 0.331061 + 0.245679i
$$485$$ 44.0403 + 44.0403i 1.99977 + 1.99977i
$$486$$ −1.34277 0.443806i −0.0609094 0.0201314i
$$487$$ 16.8200i 0.762186i 0.924537 + 0.381093i $$0.124452\pi$$
−0.924537 + 0.381093i $$0.875548\pi$$
$$488$$ −19.5867 + 13.7819i −0.886646 + 0.623876i
$$489$$ 4.86054i 0.219801i
$$490$$ 3.94244 11.9282i 0.178101 0.538860i
$$491$$ 6.10641 + 6.10641i 0.275578 + 0.275578i 0.831341 0.555763i $$-0.187574\pi$$
−0.555763 + 0.831341i $$0.687574\pi$$
$$492$$ 11.6364 1.72269i 0.524611 0.0776649i
$$493$$ 0.417438 0.417438i 0.0188005 0.0188005i
$$494$$ 0.555677 0.279604i 0.0250011 0.0125800i
$$495$$ −9.65685 −0.434043
$$496$$ −2.13368 7.04836i −0.0958050 0.316481i
$$497$$ 9.32206 0.418151
$$498$$ −18.0727 + 9.09378i −0.809857 + 0.407502i
$$499$$ −19.6770 + 19.6770i −0.880864 + 0.880864i −0.993622 0.112758i $$-0.964031\pi$$
0.112758 + 0.993622i $$0.464031\pi$$
$$500$$ 4.92153 + 33.2440i 0.220098 + 1.48672i
$$501$$ −15.3458 15.3458i −0.685601 0.685601i
$$502$$ −6.54856 + 19.8132i −0.292277 + 0.884308i
$$503$$ 25.7308i 1.14728i 0.819108 + 0.573639i $$0.194469\pi$$
−0.819108 + 0.573639i $$0.805531\pi$$
$$504$$ −6.01606 1.04655i −0.267977 0.0466172i
$$505$$ 0.439861i 0.0195736i
$$506$$ −9.65685 3.19173i −0.429300 0.141890i
$$507$$ 6.48462 + 6.48462i 0.287992 + 0.287992i
$$508$$ 4.54789 6.12845i 0.201780 0.271906i
$$509$$ 1.73514 1.73514i 0.0769087 0.0769087i −0.667606 0.744515i $$-0.732681\pi$$
0.744515 + 0.667606i $$0.232681\pi$$
$$510$$ 0.542661 + 1.07847i 0.0240294 + 0.0477553i
$$511$$ 12.8991 0.570623
$$512$$ −19.6734 11.1784i −0.869450 0.494021i
$$513$$ −0.224777 −0.00992417
$$514$$ −0.471775 0.937591i −0.0208091 0.0413554i
$$515$$ 35.8538 35.8538i 1.57991 1.57991i
$$516$$ 13.0711 17.6137i 0.575422 0.775401i
$$517$$ −5.08532 5.08532i −0.223652 0.223652i
$$518$$ 15.0440 + 4.97226i 0.660995 + 0.218469i
$$519$$ 12.3695i 0.542959i
$$520$$ 20.7101 + 3.60272i 0.908196 + 0.157990i
$$521$$ 33.5944i 1.47180i 0.677092 + 0.735898i $$0.263240\pi$$
−0.677092 + 0.735898i $$0.736760\pi$$
$$522$$ −1.16559 + 3.52660i −0.0510166 + 0.154355i
$$523$$ −21.8158 21.8158i −0.953938 0.953938i 0.0450467 0.998985i $$-0.485656\pi$$
−0.998985 + 0.0450467i $$0.985656\pi$$
$$524$$ −0.317883 2.14724i −0.0138868 0.0938026i
$$525$$ −14.3871 + 14.3871i −0.627907 + 0.627907i
$$526$$ −6.92839 + 3.48621i −0.302092 + 0.152006i
$$527$$ −0.413828 −0.0180266
$$528$$ −2.94680 9.73439i −0.128243 0.423635i
$$529$$ 15.0000 0.652174
$$530$$ 50.9846 25.6543i 2.21463 1.11435i
$$531$$ 4.00000 4.00000i 0.173585 0.173585i
$$532$$ −0.960099 + 0.142136i −0.0416256 + 0.00616236i
$$533$$ −8.13853 8.13853i −0.352519 0.352519i
$$534$$ 0.633962 1.91811i 0.0274342 0.0830046i
$$535$$ 39.0907i 1.69004i
$$536$$ 34.1013 23.9949i 1.47295 1.03642i
$$537$$ 11.6413i 0.502359i
$$538$$ 27.4858 + 9.08445i 1.18500 + 0.391658i
$$539$$ 4.20531 + 4.20531i 0.181136 + 0.181136i
$$540$$ −6.09976 4.52660i −0.262492 0.194794i
$$541$$ 27.2112 27.2112i 1.16990 1.16990i 0.187669 0.982232i $$-0.439907\pi$$
0.982232 0.187669i $$-0.0600933\pi$$
$$542$$ −8.92281 17.7329i −0.383267 0.761694i
$$543$$ 9.50732 0.407998
$$544$$ −0.921533 + 0.876113i −0.0395104 + 0.0375630i
$$545$$ 37.8155 1.61984
$$546$$ 2.68554 + 5.33717i 0.114931 + 0.228410i
$$547$$ −6.80116 + 6.80116i −0.290796 + 0.290796i −0.837395 0.546598i $$-0.815922\pi$$
0.546598 + 0.837395i $$0.315922\pi$$
$$548$$ −8.52841 6.32889i −0.364315 0.270357i
$$549$$ −5.98737 5.98737i −0.255535 0.255535i
$$550$$ −32.1765 10.6348i −1.37201 0.453470i
$$551$$ 0.590346i 0.0251496i
$$552$$ −4.60365 6.54266i −0.195944 0.278474i
$$553$$ 32.4004i 1.37780i
$$554$$ −5.95635 + 18.0214i −0.253061 + 0.765657i
$$555$$ 13.9365 + 13.9365i 0.591570 + 0.591570i
$$556$$ −24.5307 + 3.63159i −1.04033 + 0.154014i
$$557$$ −4.29337 + 4.29337i −0.181916 + 0.181916i −0.792190 0.610274i $$-0.791059\pi$$
0.610274 + 0.792190i $$0.291059\pi$$
$$558$$ 2.32581 1.17030i 0.0984594 0.0495426i
$$559$$ −21.4609 −0.907701
$$560$$ −28.9164 15.4775i −1.22194 0.654044i
$$561$$ −0.571533 −0.0241301
$$562$$ −4.91878 + 2.47502i −0.207486 + 0.104402i
$$563$$ −10.0801 + 10.0801i −0.424825 + 0.424825i −0.886861 0.462036i $$-0.847119\pi$$
0.462036 + 0.886861i $$0.347119\pi$$
$$564$$ −0.828427 5.59587i −0.0348831 0.235628i
$$565$$ −50.6187 50.6187i −2.12954 2.12954i
$$566$$ 7.83621 23.7091i 0.329381 0.996569i
$$567$$ 2.15894i 0.0906670i
$$568$$ −2.09311 + 12.0321i −0.0878248 + 0.504856i
$$569$$ 32.5018i 1.36255i −0.732029 0.681274i $$-0.761426\pi$$
0.732029 0.681274i $$-0.238574\pi$$
$$570$$ −1.14631 0.378872i −0.0480137 0.0158692i
$$571$$ −9.17157 9.17157i −0.383818 0.383818i 0.488657 0.872476i $$-0.337487\pi$$
−0.872476 + 0.488657i $$0.837487\pi$$
$$572$$ −5.93030 + 7.99129i −0.247958 + 0.334132i
$$573$$ −14.7101 + 14.7101i −0.614522 + 0.614522i
$$574$$ 8.07174 + 16.0415i 0.336908 + 0.669560i
$$575$$ −26.6559 −1.11163
$$576$$ 2.70160 7.53003i 0.112567 0.313751i
$$577$$ 11.7536 0.489308 0.244654 0.969611i $$-0.421326\pi$$
0.244654 + 0.969611i $$0.421326\pi$$
$$578$$ −10.7742 21.4123i −0.448147 0.890634i
$$579$$ 10.0023 10.0023i 0.415681 0.415681i
$$580$$ −11.8885 + 16.0202i −0.493643 + 0.665201i
$$581$$ −21.8395 21.8395i −0.906053 0.906053i
$$582$$ −22.0202 7.27798i −0.912765 0.301682i
$$583$$ 27.0192i 1.11902i
$$584$$ −2.89627 + 16.6491i −0.119849 + 0.688943i
$$585$$ 7.43208i 0.307279i
$$586$$ 7.00144 21.1835i 0.289227 0.875081i
$$587$$ 6.46002 + 6.46002i 0.266634 + 0.266634i 0.827742 0.561109i $$-0.189625\pi$$
−0.561109 + 0.827742i $$0.689625\pi$$
$$588$$ 0.685069 + 4.62751i 0.0282518 + 0.190835i
$$589$$ 0.292621 0.292621i 0.0120572 0.0120572i
$$590$$ 27.1412 13.6569i 1.11739 0.562244i
$$591$$ −3.43463 −0.141282
$$592$$ −9.79564 + 18.3011i −0.402598 + 0.752170i
$$593$$ 5.49270 0.225558 0.112779 0.993620i $$-0.464025\pi$$
0.112779 + 0.993620i $$0.464025\pi$$
$$594$$ 3.21215 1.61628i 0.131796 0.0663168i
$$595$$ −1.30324 + 1.30324i −0.0534278 + 0.0534278i
$$596$$ 2.87820 0.426097i 0.117896 0.0174536i
$$597$$ 0.216503 + 0.216503i 0.00886089 + 0.00886089i
$$598$$ −2.45641 + 7.43208i −0.100450 + 0.303920i
$$599$$ 36.4348i 1.48868i 0.667799 + 0.744342i $$0.267237\pi$$
−0.667799 + 0.744342i $$0.732763\pi$$
$$600$$ −15.3393 21.8001i −0.626225 0.889985i
$$601$$ 9.97474i 0.406878i −0.979088 0.203439i $$-0.934788\pi$$
0.979088 0.203439i $$-0.0652119\pi$$
$$602$$ 31.7928 + 10.5080i 1.29578 + 0.428274i
$$603$$ 10.4243 + 10.4243i 0.424510 + 0.424510i
$$604$$ 3.27151 + 2.42777i 0.133116 + 0.0987848i
$$605$$ −12.1786 + 12.1786i −0.495131 + 0.495131i
$$606$$ 0.0736202 + 0.146310i 0.00299061 + 0.00594345i
$$607$$ 4.51900 0.183421 0.0917103 0.995786i $$-0.470767\pi$$
0.0917103 + 0.995786i $$0.470767\pi$$
$$608$$ 0.0321169 1.27113i 0.00130251 0.0515510i
$$609$$ −5.67016 −0.229766
$$610$$ −20.4422 40.6261i −0.827679 1.64490i
$$611$$ −3.91375 + 3.91375i −0.158333 + 0.158333i
$$612$$ −0.361009 0.267903i −0.0145929 0.0108293i
$$613$$ −8.43692 8.43692i −0.340764 0.340764i 0.515890 0.856655i $$-0.327461\pi$$
−0.856655 + 0.515890i $$0.827461\pi$$
$$614$$ −10.2605 3.39125i −0.414080 0.136860i
$$615$$ 22.3380i 0.900757i
$$616$$ 12.6981 8.93484i 0.511621 0.359995i
$$617$$ 32.1201i 1.29311i 0.762869 + 0.646554i $$0.223790\pi$$
−0.762869 + 0.646554i $$0.776210\pi$$
$$618$$ −5.92510 + 17.9269i −0.238343 + 0.721126i
$$619$$ 15.0412 + 15.0412i 0.604559 + 0.604559i 0.941519 0.336960i $$-0.109399\pi$$
−0.336960 + 0.941519i $$0.609399\pi$$
$$620$$ 13.8337 2.04797i 0.555573 0.0822486i
$$621$$ 2.00000 2.00000i 0.0802572 0.0802572i
$$622$$ 30.5243 15.3591i 1.22391 0.615845i
$$623$$ 3.08398 0.123557
$$624$$ −7.49175 + 2.26790i −0.299910 + 0.0907888i
$$625$$ −16.6958 −0.667833
$$626$$ 20.9841 10.5587i 0.838692 0.422011i
$$627$$ 0.404135 0.404135i 0.0161396 0.0161396i
$$628$$ 2.52413 + 17.0500i 0.100724 + 0.680368i
$$629$$ 0.824818 + 0.824818i 0.0328876 + 0.0328876i
$$630$$ 3.63899 11.0101i 0.144981 0.438652i
$$631$$ 36.4685i 1.45179i −0.687807 0.725894i $$-0.741426\pi$$
0.687807 0.725894i $$-0.258574\pi$$
$$632$$ −41.8196 7.27494i −1.66350 0.289382i
$$633$$ 10.2284i 0.406542i
$$634$$ 3.44035 + 1.13709i 0.136634 + 0.0451595i
$$635$$ 10.2475 + 10.2475i 0.406659 + 0.406659i
$$636$$ −12.6651 + 17.0667i −0.502205 + 0.676739i
$$637$$ 3.23648 3.23648i 0.128234 0.128234i
$$638$$ −4.24494 8.43625i −0.168059 0.333994i
$$639$$ −4.31788 −0.170813
$$640$$ 26.4697 33.8477i 1.04631 1.33795i
$$641$$ 14.0036 0.553109 0.276555 0.960998i $$-0.410807\pi$$
0.276555 + 0.960998i $$0.410807\pi$$
$$642$$ −6.54266 13.0027i −0.258218 0.513175i
$$643$$ 16.6034 16.6034i 0.654774 0.654774i −0.299365 0.954139i $$-0.596775\pi$$
0.954139 + 0.299365i $$0.0967748\pi$$
$$644$$ 7.27798 9.80734i 0.286793 0.386463i
$$645$$ 29.4522 + 29.4522i 1.15968 + 1.15968i
$$646$$ −0.0678434 0.0224232i −0.00266926 0.000882230i
$$647$$ 12.1908i 0.479270i −0.970863 0.239635i $$-0.922972\pi$$
0.970863 0.239635i $$-0.0770277\pi$$
$$648$$ 2.78658 + 0.484753i 0.109467 + 0.0190429i
$$649$$ 14.3835i 0.564600i
$$650$$ −8.18473 + 24.7636i −0.321032 + 0.971309i
$$651$$ 2.81056 + 2.81056i 0.110155 + 0.110155i
$$652$$ 1.42362 + 9.61628i 0.0557533 + 0.376603i
$$653$$ 0.983270 0.983270i 0.0384783 0.0384783i −0.687606 0.726084i $$-0.741338\pi$$
0.726084 + 0.687606i $$0.241338\pi$$
$$654$$ −12.5785 + 6.32924i −0.491859 + 0.247493i
$$655$$ 4.12198 0.161059
$$656$$ −22.5174 + 6.81647i −0.879157 + 0.266138i
$$657$$ −5.97474 −0.233097
$$658$$ 7.71423 3.88163i 0.300732 0.151322i
$$659$$ −18.0559 + 18.0559i −0.703357 + 0.703357i −0.965130 0.261772i $$-0.915693\pi$$
0.261772 + 0.965130i $$0.415693\pi$$
$$660$$ 19.1055 2.82843i 0.743680 0.110096i
$$661$$ −4.55890 4.55890i −0.177321 0.177321i 0.612866 0.790187i $$-0.290017\pi$$
−0.790187 + 0.612866i $$0.790017\pi$$
$$662$$ −8.48889 + 25.6839i −0.329930 + 0.998232i
$$663$$ 0.439861i 0.0170828i
$$664$$ 33.0922 23.2848i 1.28423 0.903627i
$$665$$ 1.84307i 0.0714710i
$$666$$ −6.96823 2.30310i −0.270013 0.0892434i
$$667$$ −5.25272 5.25272i −0.203386 0.203386i
$$668$$ 34.8554 + 25.8661i 1.34860 + 1.00079i
$$669$$ −1.21557 + 1.21557i −0.0469968 + 0.0469968i
$$670$$ 35.5908 + 70.7320i 1.37499 + 2.73261i
$$671$$ 21.5298 0.831148
$$672$$ 12.2089 + 0.308476i 0.470969 + 0.0118997i
$$673$$ −10.8569 −0.418504 −0.209252 0.977862i $$-0.567103\pi$$
−0.209252 + 0.977862i $$0.567103\pi$$
$$674$$ −0.715856 1.42267i −0.0275737 0.0547992i
$$675$$ 6.66398 6.66398i 0.256497 0.256497i
$$676$$ −14.7287 10.9301i −0.566489 0.420389i
$$677$$ 23.7066 + 23.7066i 0.911120 + 0.911120i 0.996360 0.0852405i $$-0.0271659\pi$$
−0.0852405 + 0.996360i $$0.527166\pi$$
$$678$$ 25.3094 + 8.36511i 0.972000 + 0.321260i
$$679$$ 35.4045i 1.35870i
$$680$$ −1.38950 1.97474i −0.0532847 0.0757277i
$$681$$ 14.3059i 0.548204i
$$682$$ −2.07754 + 6.28577i −0.0795530 + 0.240694i
$$683$$ −17.8337 17.8337i −0.682386 0.682386i 0.278151 0.960537i $$-0.410278\pi$$
−0.960537 + 0.278151i $$0.910278\pi$$
$$684$$ 0.444708 0.0658358i 0.0170038 0.00251729i
$$685$$ 14.2605 14.2605i 0.544866 0.544866i
$$686$$ −25.4710 + 12.8165i −0.972489 + 0.489335i
$$687$$ −16.9981 −0.648519
$$688$$ −20.7013 + 38.6761i −0.789231 + 1.47451i
$$689$$ 20.7945 0.792205
$$690$$ 13.5706 6.82843i 0.516624 0.259954i
$$691$$ 10.8557 10.8557i 0.412970 0.412970i −0.469802 0.882772i $$-0.655675\pi$$
0.882772 + 0.469802i $$0.155675\pi$$
$$692$$ −3.62293 24.4722i −0.137723 0.930294i
$$693$$ 3.88163 + 3.88163i 0.147451 + 0.147451i
$$694$$ −13.0509 + 39.4866i −0.495406 + 1.49889i
$$695$$ 47.0907i 1.78625i
$$696$$ 1.27314 7.31856i 0.0482581 0.277409i
$$697$$ 1.32206i 0.0500765i
$$698$$ −36.6225 12.1043i −1.38618 0.458154i
$$699$$ −9.45963 9.45963i −0.357796 0.357796i
$$700$$ 24.2502 32.6780i 0.916570 1.23511i
$$701$$ −6.08875 + 6.08875i −0.229969 + 0.229969i −0.812680 0.582711i $$-0.801992\pi$$
0.582711 + 0.812680i $$0.301992\pi$$
$$702$$ −1.24392 2.47212i −0.0469486 0.0933042i
$$703$$ −1.16647 −0.0439942
$$704$$ 8.68119 + 18.3958i 0.327185 + 0.693317i
$$705$$ 10.7422 0.404574
$$706$$ 16.2672 + 32.3288i 0.612222 + 1.21671i
$$707$$ −0.176805 + 0.176805i −0.00664943 + 0.00664943i
$$708$$ −6.74218 + 9.08532i −0.253386 + 0.341447i
$$709$$ 22.8836 + 22.8836i 0.859413 + 0.859413i 0.991269 0.131856i $$-0.0420936\pi$$
−0.131856 + 0.991269i $$0.542094\pi$$
$$710$$ −22.0202 7.27798i −0.826402 0.273138i
$$711$$ 15.0075i 0.562826i
$$712$$ −0.692453 + 3.98053i −0.0259508 + 0.149177i
$$713$$ 5.20730i 0.195015i
$$714$$ 0.215371 0.651622i 0.00806004 0.0243863i
$$715$$ −13.3624 13.3624i −0.499724 0.499724i
$$716$$ 3.40965 + 23.0316i 0.127425 + 0.860729i
$$717$$ 9.45223 9.45223i 0.353000 0.353000i
$$718$$ −4.76638 + 2.39834i −0.177880 + 0.0895052i
$$719$$ −1.46744 −0.0547262 −0.0273631 0.999626i $$-0.508711\pi$$
−0.0273631 + 0.999626i $$0.508711\pi$$
$$720$$ 13.3938 + 7.16902i 0.499157 + 0.267174i
$$721$$ −28.8233 −1.07344
$$722$$ −23.9389 + 12.0455i −0.890913 + 0.448288i
$$723$$ 0.149535 0.149535i 0.00556126 0.00556126i
$$724$$ −18.8096 + 2.78463i −0.699055 + 0.103490i
$$725$$ −17.5020 17.5020i −0.650008 0.650008i
$$726$$ 2.01260 6.08930i 0.0746947 0.225995i
$$727$$ 15.3928i 0.570889i 0.958395 + 0.285445i $$0.0921412\pi$$
−0.958395 + 0.285445i $$0.907859\pi$$
$$728$$ −6.87640 9.77267i −0.254856 0.362199i
$$729$$ 1.00000i 0.0370370i
$$730$$ −30.4697 10.0707i −1.12773 0.372733i
$$731$$ 1.74311 + 1.74311i 0.0644711 + 0.0644711i
$$732$$ 13.5993 + 10.0920i 0.502644 + 0.373010i
$$733$$ −12.4185 + 12.4185i −0.458688 + 0.458688i −0.898225 0.439536i $$-0.855143\pi$$
0.439536 + 0.898225i $$0.355143\pi$$
$$734$$ −17.4473 34.6743i −0.643993 1.27985i
$$735$$ −8.88325 −0.327664
$$736$$ 11.0243 + 11.5959i 0.406362 + 0.427429i
$$737$$ −37.4844 −1.38075
$$738$$ −3.73875 7.43027i −0.137625 0.273512i
$$739$$ −14.6559 + 14.6559i −0.539127 + 0.539127i −0.923273 0.384146i $$-0.874496\pi$$
0.384146 + 0.923273i $$0.374496\pi$$
$$740$$ −31.6543 23.4905i −1.16364 0.863528i
$$741$$ −0.311029 0.311029i −0.0114259 0.0114259i
$$742$$ −30.8055 10.1817i −1.13090 0.373780i
$$743$$ 31.7821i 1.16597i −0.812482 0.582986i $$-0.801884\pi$$
0.812482 0.582986i $$-0.198116\pi$$
$$744$$ −4.25870 + 2.99657i −0.156131 + 0.109860i
$$745$$ 5.52518i 0.202427i
$$746$$ −7.92273 + 23.9709i −0.290072 + 0.877637i
$$747$$ 10.1158 + 10.1158i 0.370118 + 0.370118i
$$748$$ 1.13074 0.167398i 0.0413440 0.00612068i
$$749$$ 15.7127 15.7127i 0.574131 0.574131i
$$750$$ 21.2275 10.6812i 0.775117 0.390022i
$$751$$ 29.7594 1.08594 0.542968 0.839753i $$-0.317301\pi$$
0.542968 + 0.839753i $$0.317301\pi$$
$$752$$ 3.27798 + 10.8284i 0.119536 + 0.394872i
$$753$$ 14.7555 0.537720
$$754$$ −6.49268 + 3.26697i −0.236449 + 0.118976i
$$755$$ −5.47036 + 5.47036i −0.199087 + 0.199087i
$$756$$ 0.632339 + 4.27133i 0.0229980 + 0.155347i
$$757$$ 15.6355 + 15.6355i 0.568282 + 0.568282i 0.931647 0.363365i $$-0.118372\pi$$
−0.363365 + 0.931647i $$0.618372\pi$$
$$758$$ 7.32361 22.1582i 0.266005 0.804822i
$$759$$ 7.19173i 0.261043i
$$760$$ 2.37887 + 0.413828i 0.0862908 + 0.0150111i
$$761$$ 4.55957i 0.165284i −0.996579 0.0826422i $$-0.973664\pi$$
0.996579 0.0826422i $$-0.0263359\pi$$
$$762$$ −5.12374 1.69347i −0.185614 0.0613480i
$$763$$ −15.2002 15.2002i −0.550284 0.550284i
$$764$$ 24.7945 33.4114i 0.897032 1.20878i
$$765$$ 0.603650 0.603650i 0.0218250 0.0218250i
$$766$$ −10.9261 21.7142i −0.394777 0.784567i
$$767$$ 11.0698 0.399706
$$768$$ −3.13946 + 15.6890i −0.113285 + 0.566127i
$$769$$ 36.5794 1.31909 0.659543 0.751667i $$-0.270750\pi$$
0.659543 + 0.751667i $$0.270750\pi$$
$$770$$ 13.2527 + 26.3380i 0.477595 + 0.949157i
$$771$$ −0.524797 + 0.524797i −0.0189001 + 0.0189001i
$$772$$ −16.8593 + 22.7185i −0.606780 + 0.817657i
$$773$$ −18.7108 18.7108i −0.672981 0.672981i 0.285421 0.958402i $$-0.407867\pi$$
−0.958402 + 0.285421i $$0.907867\pi$$
$$774$$ −14.7261 4.86720i −0.529319